Walters beat Lukasz Fabianski with a nicely executed header from fellow substitute Oussama Assaidi's cross in the 76th minute after each side had scored a contentious penalty in the first half
The Potters fell behind in the 34th minute when Wilfried Bony hit the turf following a tussle with Ryan Shawcross at a corner and referee Michael Oliver awarded a spot-kick which the Swans striker dispatched himself
Oliver then made what looked an even more debatable decision, judging it to be a foul as Victor Moses went down under the attentions of Angel Rangel in the area, with Charlie Adam tucking away the resulting penalty in the 43rd minute.
The victory Mark Hughes' men went on to secure was just about deserved overall and they move up to 10th in the table, level on points with Garry Monk's eighth-placed men.
Swansea put some decent passing moves together in the opening stages of the contest, with one seeing Wayne Routledge turn and play in Gylfi Sigurdsson, who miscued as he tried to go around Asmir Begovic and the ball went out of play.
An even better one moments later was started by Ki Sung-yueng and when the ball came back to the South Korea international, he struck a shot with came back off Begovic's legs
Stoke immediately raced up the other end and Adam drilled an effort wide.
As the hosts looked to get control of the game, Moses swung a delivery across the box and Peter Crouch tried to jump to meet it
He failed to make contact and appealed for a penalty, claiming his shirt had been held by Neil Taylor, but - on this occasion - nothing was given.
Around 10 minutes later, though, Oliver was convinced there had been an infringement when Shawcross and Bony got to grips with each other as a corner came into the Stoke box and the latter went to ground
The Potters skipper was booked, the penalty was given and Bony stepped up to calmly convert it, sending Begovic the wrong way.
If there were questions over that decision, there were even more about Oliver's call to point to the spot again just prior to the break.
Stoke had been pressing once more, with Adam having just sent a low shot into Fabianski, and Moses burst into the box from the left flank
He subsequently hit the deck as Rangel came in to challenge him and although it seemed the on-loan Chelsea winger might have gone down a little easily, Oliver saw it as a foul
Adam made no mistake with the spot-kick.
The home side looked eager to add another as the second half got under way, with Phil Bardsley lashing a wild effort off target and Adam shooting over from outside the box.
Moses then sent a corner bouncing across the face of goal and Crouch met it with his head at the back post but could not keep his effort down.
Soon after, a scramble in the Stoke area from a Swansea free-kick saw the ball come to Ki in front of goal, but Begovic dealt with his shot
Bony then, somewhat optimistically, went down in the box again as Marc Wilson marked him at a corner, with Oliver unmoved.
It appeared anyone's game to win and it was the Potters who seized the moment with just under a quarter of an hour to go
Rangel gave the ball away, Stoke surged forward and Assaidi - on for Moses - crossed well to Walters, who directed a fine header past Fabianski.
Swansea pushed for a leveller at the end, but efforts from Ki, Bony and substitute Bafetimbi Gomis were unsuccessful.
Source : PA
Source: PA